Question: Simplify the following expression: $p = \dfrac{-5r^2 - 65r - 200}{r + 8} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-5$ , so we can rewrite the expression: $ p =\dfrac{-5(r^2 + 13r + 40)}{r + 8} $ Then we factor the remaining polynomial: $r^2 + {13}r + {40} $ ${8} + {5} = {13}$ ${8} \times {5} = {40}$ $ (r + {8}) (r + {5}) $ This gives us a factored expression: $\dfrac{-5(r + {8}) (r + {5})}{r + 8}$ We can divide the numerator and denominator by $(r - 8)$ on condition that $r \neq -8$ Therefore $p = -5(r + 5); r \neq -8$